2(r+1)=3(r-1)

Solution for 2(r+1)=3(r-1) equation:

Simplifying
2(r + 1) = 3(r + -1)

Reorder the terms:
2(1 + r) = 3(r + -1)
(1 * 2 + r * 2) = 3(r + -1)
(2 + 2r) = 3(r + -1)

Reorder the terms:
2 + 2r = 3(-1 + r)
2 + 2r = (-1 * 3 + r * 3)
2 + 2r = (-3 + 3r)

Solving
2 + 2r = -3 + 3r

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-3r' to each side of the equation.
2 + 2r + -3r = -3 + 3r + -3r

Combine like terms: 2r + -3r = -1r
2 + -1r = -3 + 3r + -3r

Combine like terms: 3r + -3r = 0
2 + -1r = -3 + 0
2 + -1r = -3

Add '-2' to each side of the equation.
2 + -2 + -1r = -3 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = -3 + -2
-1r = -3 + -2

Combine like terms: -3 + -2 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5